Which of the following is an irrational number?

Which of the following is an irrational number?

• A. 3/4
• B. √2
• C. 0.25
• D. -2

Answer: (B)

An irrational number is defined as a number that cannot be expressed as a simple fraction or as a ratio of two integers. These numbers have non-repeating, non-terminating decimal expansions. The square root of 2 (√2) is an example of an irrational number because it cannot be written as a fraction and its decimal form is approximately 1.41421356..., which continues infinitely without repeating. In contrast, the other options represent different types of numbers. The fraction 3/4 is a ration number because it can be expressed as the ratio of the integers 3 and 4. The decimal 0.25 is also a rational number because it can be expressed as the fraction 1/4. Finally, -2 is a rational number as it can be expressed as -2/1, showing it is also the ratio of two integers. Thus, the only irrational number among the choices is √2.

An irrational number is defined as a number that cannot be expressed as a simple fraction or as a ratio of two integers. These numbers have non-repeating, non-terminating decimal expansions. The square root of 2 (√2) is an example of an irrational number because it cannot be written as a fraction and its decimal form is approximately 1.41421356..., which continues infinitely without repeating.

In contrast, the other options represent different types of numbers. The fraction 3/4 is a ration number because it can be expressed as the ratio of the integers 3 and 4. The decimal 0.25 is also a rational number because it can be expressed as the fraction 1/4. Finally, -2 is a rational number as it can be expressed as -2/1, showing it is also the ratio of two integers. Thus, the only irrational number among the choices is √2.